The density of silver is 10.5 g/cm3. What is the mass (in kilo-grams) of a cube of silver that measures 0.62 m on each side?

검증된 단계별 안내

Step 1: Convert the side length of the cube from meters to centimeters. Since 1 meter is equal to 100 centimeters, you can do this by multiplying the given length in meters by 100.

Step 2: Calculate the volume of the cube in cubic centimeters (cm^3). The volume of a cube is given by the formula side length^3.

Step 3: Use the given density of silver to find the mass of the cube in grams. Density is defined as mass/volume, so you can find the mass by multiplying the density by the volume.

Step 4: Convert the mass from grams to kilograms. Since 1 kilogram is equal to 1000 grams, you can do this by dividing the mass in grams by 1000.

Step 5: The result from step 4 is the mass of the silver cube in kilograms.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Density

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). It is a physical property that helps determine how much mass is contained in a given volume of a substance. In this question, the density of silver is provided, which will be used to calculate the mass of the silver cube.

Volume of a Cube

The volume of a cube is calculated using the formula V = s³, where 's' is the length of one side of the cube. This formula allows us to determine how much space the cube occupies. In this case, the side length of the silver cube is given in meters, so it must be converted to centimeters to match the density units for accurate calculations.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another set of units. In this problem, it is necessary to convert the volume from cubic centimeters to cubic meters and the mass from grams to kilograms. Understanding how to perform these conversions is essential for ensuring that calculations yield results in the desired units.